Question

If ln x + ln(x-7)= ln6x, then x= ??
show working out

Answer 1

\[lnx+\ln(x-7)=lnx(x-7)\]
so
\[\ln(x^2-7x)=\ln(6x)\]
If the logs are equal and the bases are the same, then the arguments must be equal.

Answer 2

\[x^2-7x=6x\]
\[x^2-13x=0\]
\[x(x-13)=0\]
\[x=0, x=13\]

Answer 3

Discard x = 0